Question: Simplify the following expression: $n = \dfrac{1}{5y} + \dfrac{1}{7y}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $5y$ and $7y$ $\lcm(5y, 7y) = 35y$ $ n = \dfrac{7}{7} \cdot \dfrac{1}{5y} + \dfrac{5}{5} \cdot \dfrac{1}{7y} $ $n = \dfrac{7}{35y} + \dfrac{5}{35y}$ $n = \dfrac{7 +5}{35y}$ $n = \dfrac{12}{35y}$